On the multi-temporal correlation betweenphotosynthesis and soil CO2 efflux: reconciling lagsand observations

Rodrigo Vargas1, Dennis D. Baldocchi2, Michael Bahn3, Paul J. Hanson4, Kevin P. Hosman5, Liisa Kulmala6,

Jukka Pumpanen6 and Bai Yang4

1Departamento de Biologıa de la Conservacion, Centro de Investigacion Cientıfica y de Educacion Superior de Ensenada (CICESE), Baja California,

Mexico; 2Department of Environmental Science Policy and Management, University of California, Berkeley, CA, USA; 3Institute of Ecology, University of

Innsbruck, Innsbruck, Austria; 4Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA; 5Department of Forestry,

University of Missouri, Columbia, MO, USA; 6Department of Forest Science, University of Helsinki, Helsinki, Finland

Author for correspondence:Rodrigo Vargas

Tel: +52 (646) 175 05 00

Email: rvargas@cicese.mx

Received: 28 February 2011

Accepted: 16 April 2011

New Phytologist (2011) 191: 1006–1017doi: 10.1111/j.1469-8137.2011.03771.x

Key words: carbon cycle, eddy covariance,forest, grassland, hysteresis, photosynthesis,soil respiration, wavelet analysis.

Summary

• Although there is increasing evidence of the temporal correlation between

photosynthesis and soil CO2 efflux, no study has so far tested its generality across

the growing season at multiple study sites and across several time scales.

• Here, we used continuous (hourly) data and applied time series analysis (wavelet

coherence analysis) to identify temporal correlations and time lags between photo-

synthesis and soil CO2 efflux for three forests from different climates and a

grassland.

• Results showed the existence of multi-temporal correlations at time periods that

varied between 1 and 16 d during the growing seasons at all study sites. Temporal

correlations were strongest at the 1 d time period, with longer time lags for forests

relative to the grassland. The multi-temporal correlations were not continuous

throughout the growing season, and were weakened when the effect of variations

in soil temperature and CO2 diffusivity on soil CO2 efflux was taken into account.

• Multi-temporal correlations between photosynthesis and soil CO2 efflux exist,

and suggest that multiple biophysical drivers (i.e. photosynthesis, soil CO2 diffu-

sion, temperature) are likely to coexist for the regulation of allocation and

transport speed of carbon during a growing season. Future studies should consider

the multi-temporal influence of these biophysical drivers to investigate their effect

on the transport of carbon through the soil–plant–atmosphere continuum.

Introduction

Canopy photosynthesis (FA) and ecosystem respiration areimportant fluxes that regulate the carbon balance of terres-trial ecosystems. Soil CO2 efflux (SR), which includesautotrophic and heterotrophic CO2 contributions (Hansonet al., 2000; Ryan & Law, 2005), represents the largestsource of CO2 from terrestrial ecosystems to the atmosphere(Raich & Potter, 1995; Schlesinger & Andrews, 2000).Consequently, predictive models of terrestrial carboncycling depend on an accurate representation of SR for thequantification of carbon fluxes (Vargas et al., 2011).

Traditionally, SR has been represented by a temperature-dependent function (Lloyd & Taylor, 1994), but multiple

studies have recognized the importance of changes in soilmoisture, as these influence plant and microbial metabolismand change soil CO2 diffusion rates (Simunek & Suarez,1993; Davidson & Trumbore, 1995; Burton et al., 1998).Recent studies have provided evidence that FA influencesSR, which challenges the assumption that most of the CO2

efflux from soils is derived from the decomposition of soilorganic matter (Hogberg et al., 2001; Kuzyakov & Cheng,2001). Short-term relationships between FA and SR havebeen consistently reported using girdling techniques(Hogberg et al., 2002; Subke et al., 2004), root exclusionby trenching (Hanson et al., 2000; Kuzyakov & Larionova,2005), clipping (Bremer et al., 1998; Bahn et al., 2006),measurements of natural abundance of ecosystem d13C

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(Ekblad & Hogberg, 2001; Bowling et al., 2002), isotopiclabeling using 13C (Carbone & Trumbore, 2007; Hogberget al., 2008; Bahn et al., 2009; Subke et al., 2009) or 14C(Carbone et al., 2007; Pumpanen et al., 2009), andecosystem carbon fluxes using the eddy covariance technique(Tang et al., 2005; Baldocchi et al., 2006; Stoy et al., 2007).

Previous studies have reported that the relationshipbetween FA and SR varies from hours to multiple days(Kuzyakov & Gavrichkova, 2010; Mencuccini & Holtta,2010). Thus, it has been argued that the differences inresults may come from the different methodologies applied.For example, isotopic techniques track molecules of carbon(13C or 14C) through the soil–plant–atmosphere contin-uum, whereas soil flux-based techniques relate the variationin FA (or a surrogate such as vapor pressure deficit or photo-synthetic active radiation) to SR. In general, isotopiclabeling techniques have been able to identify the relativelyslow (i.e. days to weeks) transport of carbon molecules fromFA to SR processes (Kuzyakov & Gavrichkova, 2010;Mencuccini & Holtta, 2010). Meanwhile, soil flux-basedtechniques have been able to identify a strong short-termcorrelation between FA of trees and SR (i.e. hours to < 2 d)because of the high temporal frequency of the measure-ments (Baldocchi et al., 2006; Stoy et al., 2007). Finally, astrong correlation between FA and SR has also beenobserved at seasonal and annual intervals (Janssens et al.,2001; Bahn et al., 2008; Vargas et al., 2010b). At the sea-sonal scale, FA and SR appear to be coupled in short-staturevegetation, but decoupled in tall-stature vegetation (Vargaset al., 2010a).

The main goal of this study was to explore at which tem-poral scales FA influences SR using continuous datasetsacross the growing season of different study sites. Here, weask two questions: (1) at which time periods (e.g. hours(1 d), days (4 d) or weeks (16 d)) are the temporal correla-tions (if any) between FA and SR most pronounced?; and

(2) do the temporal correlations remain constant through-out the growing seasons of different vegetation types, or arethey influenced by changes in photosynthetic capacity, soiltemperature and soil moisture?

We hypothesize that FA influences SR at multiple timeperiods (potentially from hours to weeks) independent ofchanges in soil temperature (Ts) and soil CO2 diffusivityamong different vegetation types. This may be possiblebecause different drivers that influence the allocationand transport speed of carbon through the soil–plant–atmosphere continuum could coexist within the growingseason. These drivers (e.g. photosynthesis, soil CO2 diffu-sion, Ts, phloem transport) have been reviewed recently(Kuzyakov & Gavrichkova, 2010; Mencuccini & Holtta,2010), but have been identified by the individual originalstudies only at one particular time. The novelty of our studyrelies on the analysis at high temporal resolution of FA andSR data (hourly intervals), and on the exploration of thepossibility of multi-temporal relationships between thesefluxes using wavelet coherence analysis (Grinsted et al.,2004; Vargas et al., 2010c) across multiple sites throughouttheir growing seasons.

Materials and Methods

Study sites

We used continuous hourly measurements of FA inferredfrom net ecosystem exchange (NEE) values using the eddycovariance technique (Goulden et al., 1996; Aubinet et al.,2000), and hourly measurements of SR during the growingseason at four study sites (Table 1). Eddy covariance data forthis study were drawn from the La Thuile 2007 FLUXNET2.0v dataset (http://www.fluxdata.org). The La Thuile data-set has been harmonized for gap filling, quality control ofNEE values and calculation of FA following standardized

Table 1 Information on location, elevation, dominant species, maximum canopy height, growing season and history of the sites included inthis study

Site name Site ID Latitude LongitudeElevation(m)

Canopyheight (m)

Growingseason(DOY) Site history Reference

Tonzi Ranch US-Ton 38.4316 )120.966 177 5.4–14.8 50–160 Grazing Ma et al. (2007)Missouri Ozark US-Moz 38.7441 )92.2 219 17–20 120–210 Undisturbed ⁄ 85

yr of naturalregeneration

Gu et al. (2006);Yang et al. (2007)

Hyytiala FI-Hyy 61.8474 24.2948 181 14 150–250 Prescribed burningin 1962

Hari & Kulmala (2005)

Neustift ⁄ StubaiValley

AT-Neu 47.11667 11.3175 970 0.05–1.0 110–265 Organic fertilizationthree cuts, grazed inlate summer

Wohlfahrt et al. (2008)

US-Ton, Mediterranean deciduous forest; US-Moz, temperate broadleaf forest; FI-Hyy, boreal evergreen forest; AT-Neu, temperate grass-land. DOY, days of the year of the growing season, defined as the days on which the ecosystem was a net carbon sink for the year 2007(Churkina et al., 2005).

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protocols (Reichstein et al., 2005; Papale et al., 2006). Thisstudy uses data from the year 2007 across all sites for whichboth eddy covariance and SR measurements were carried outduring the growing season (Supporting InformationMethods S1). The SR measurements presented in this studyhave not been published previously for any site.

The sites included the following: Mediterranean decidu-ous woodland (US-Ton), temperate broadleaf forest(US-Moz), boreal evergreen forest (FI-Hyy) and temperategrassland (AT-Neu). FA was not manipulated directly, butwe took advantage of its variation during the whole growingseason and explored a range of time scales from days toweeks. Throughout the growing season, rapid changes in FA

were expected as a result of changes in phenology and syn-optic events (e.g. rainfall, cloudiness) that influenceatmospheric vapor pressure deficit and stomatal conduc-tance (Baldocchi et al., 2001; Bowling et al., 2002). Thegrowing seasons were defined as the carbon uptake periods(Fig. 1; Table 1), which were the days during which theecosystem was a net carbon sink (Churkina et al., 2005) forthe year 2007.

The deciduous woodland (US-Ton) is located in thelower foothills of the Sierra Nevada Mountains, CA, USA.The site is dominated by Quercus douglasii Hook. & Arn.,and experiences a Mediterranean-type climate with dry, hotsummers and rainy, mild winters (Table 1). FA was inferredfrom NEE measured with a three-dimensional sonic anemo-meter (Model 1352; Gill Instruments Ltd, Lymington, UK)and an open-path CO2 ⁄ H2O infrared gas analyzer (LI7500;Li-Cor Inc., Lincoln, NE, USA) installed above the stand ata height of 23 m (Ma et al., 2007). SR was calculated using

solid-state CO2 sensors installed at 2, 8 and 16 cm depthsusing the gradient flux method as described previously(Vargas et al., 2010a). Soil characteristics are defined inTable 2, and more detailed instrumentation and site infor-mation can be found elsewhere (Ma et al., 2007).

The temperate broadleaf forest (US-Moz) is located incentral Missouri (30 km southeast of Columbia), USA andis dominated by Quercus alba L. (Table 1). FA was inferredfrom NEE measured with a three-dimensional sonic ane-mometer (81000; RM Young, Traverse City, MI, USA)and an open-path CO2 ⁄ H2O infrared gas analyzer (LI7500,Li-Cor Inc.) installed at a height of 32 m above the ground(Gu et al., 2006; Yang et al., 2007). SR was calculatedusing automated SR chambers located within the footprintof the flux tower (Edwards & Riggs, 2003). Soil characteristicsare defined in Table 2, and more detailed instrumentationand site information can be found in previous studies (Guet al., 2006; Yang et al., 2007).

The boreal evergreen forest (FI-Hyy) is located at theHyytiala Forestry Field Station, Finland, and is part of theCarboEurope network. This is a managed stand dominatedby Scots pine (Pinus sylvestris L.), established in 1962 bysowing after the area had first been treated with prescribedburning and mechanical soil preparation. FA was inferredfrom NEE measured with a three-dimensional sonic ane-mometer (R3IA; Gill Instruments Ltd) and a closed-pathCO2 ⁄ H2O infrared gas analyzer (LI6262; Li-Cor Inc.)installed above the stand at a height of 23 m. The instru-mentation is documented in more detail in Vesala et al.(2005). SR was calculated using automatic chambersbased on the closed dynamic chamber technique. The soil

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o) (p)

Fig. 1 Normalized values of daily averagesof canopy photosynthesis (FA) (a–d), soiltemperature at the depth of maximumcorrelation with soil CO2 efflux (Ts) (e–h), soilwater content (SWC) (i–l) and soil CO2 efflux(SR) (m–p) at four study sites during theirrespective growing seasons. For descriptionsof sites, see Tables 1 and 2. Days of the year(DOY), days after January 1st of the year inwhich data were collected. Normalizationwas performed on the basis of the maximumvalues of daily averages for each variable ateach study site.

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characteristics are defined in Table 2, and more detailedinstrumentation and site information can be found in previ-ous studies (Pumpanen et al., 2003; Hari & Kulmala,2005; Vesala et al., 2005).

The temperate grassland (AT-Neu) is located in ameadow in the vicinity of the village Neustift in the StubaiValley, Austria. The vegetation consists mainly of a fewdominant graminoids [Dactylis glomerata L., Festucapratensis Huds., Phleum pratensis L., Trisetum flavescens (L.)Beauv.] and forbs (Ranunculus acris L., Taraxacum officinaleG.H. Weber ex Wiggers, Trifolium pretense L., Trifoliumrepens L., Carum carvi L.). FA was inferred from NEE mea-sured with a three-dimensional sonic anemometer (R3IA;Gill Instruments) and a closed-path infrared gas analyzer(Li-6262; Li-Cor) installed above the grassland at a heightof 3 m (Wohlfahrt et al., 2008). SR was calculated usingsolid-state CO2 sensors installed at 5 and 10 cm depth,employing the gradient flux method as described previously(Vargas et al., 2010a). Soil characteristics are defined inTable 2, and more detailed instrumentation and site infor-mation can be found in previous studies (Bahn et al., 2008;Wohlfahrt et al., 2008).

Wavelet analysis

We used wavelet analysis as a time series technique that hasbeen widely applied in the geosciences (Torrence &Compo, 1998) and recently for SR research (Vargas et al.,2010c, 2011). This technique is used to quantify the spec-tral characteristics of time series that may be nonstationaryand heteroscedastic. Previous studies have used Fouriertransform (Tang et al., 2005; Baldocchi et al., 2006) andcross-correlation (Stoy et al., 2007; Vargas et al., 2010a)analysis to investigate the spectral properties of SR signals.However, these analyses failed in the presence of nonsta-tionary phenomena (Katul et al., 2001), such as rain pulses,heat waves or freezing events. Most biometeorological vari-ables (e.g. SR, FA) typically violate the stationaryassumption underlying the analysis of spectral propertiesand wavelet analysis is an alternative technique (Torrence &Compo, 1998).

In this study, we explored the temporal correlationbetween any two time series (e.g. SR with FA) using waveletcoherence analysis (Grinsted et al., 2004) (Methods S1).Previous reports have described the technique in detail forclimate studies (Torrence & Compo, 1998; Grinsted et al.,2004) and SR research (Vargas et al., 2010c). Briefly, coher-ency is roughly similar to classical correlation, but itpertains to the oscillating components in a given time per-iod (e.g. 1 d, 8 d). There are two main advantages of usingwavelet coherence analysis. First, it is possible to determinethe multi-temporal correlation between two time series.Therefore, one can identify periodicities (e.g. 1 d, 2 d, …,n d time periods) with high temporal correlations betweenthe two original time series. Second, it is possible to quan-tify the phase differences or time lags between two timeseries. Therefore, one can calculate the time lag betweentwo time series at each period that has been identified withhigh temporal correlation between them.

The phase difference represents whether or not two timeseries tend to oscillate simultaneously, rising and fallingtogether within a given time period (in phase, and thereforeshowing no time lags), or rise and fall out of phase within agiven time period (therefore showing a time lag betweenthem). From all wavelet coherence analyses, we extractedthe percentage of days with significant temporal correlationsand calculated the phase difference (time lags) at 1, 2, 4, 8,12 and 16 d time periods within the cone of influence. Thecone of influence is the region in which the wavelet trans-form suffers from edge effects because of incomplete timelocality across frequencies (Torrence & Compo, 1998);thus, the results outside the cone of influence must be inter-preted carefully. The statistical significance (5% significancelevel) of common power between any two time series wasassessed within the cone of influence of the wavelet coher-ence analysis using Monte Carlo simulations of white noisetime series (Torrence & Webster, 1999). Further details ofthe applied wavelet coherence analysis are given inMethods S1.

From a time series analysis approach, the delay betweentwo time series can provide information on the nature andorigin of coupling between the processes, and causality

Table 2 Climate and soil characteristics of the sites included in this study

Site Site ID ClimateMAP(mm)

MAT(�C) Soil type

Sand(%)

Silt(%)

Clay(%)

Bulkdensity(mg m)3)

Soilporosity(m3 m)3)

Mediterranean deciduousforest

US-Ton Csa 562 16.5 Lithic haploxerepts 37.5 45 17.5 1.58 0.4

Temperate broadleafforest

US-Moz Cfa 985 12.11 Hapludalt & argiudoll 10.5 60 29.5 0.9–1.59 0.45

Boreal evergreen forest FI-Hyy Dfc 709 3.8 Haplic podzol 65.1 28.3 6.6 0.6 0.61Temperate grassland AT-Neu Cfb 1097 3 Gleyic fluvisol 41.9 30.8 27.3 0.91 0.66

MAP, mean annual precipitation; MAT, mean annual temperature. Sand (%) includes soil fraction > 2 mm in FI-Hyy. Climate acronyms arebased on the Koppen climate classification.

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under the assumption that the effect must follow the cause.We raise caution over the use of the word ‘lag’. In isotopestudies, ‘lag’ has been used to define the time elapsedbetween the labeling and recovery of the isotope. In thisstudy, the ‘lags’ associated with the transport of carbonmolecules are interpreted as the temporal correlation atdifferent ‘time periods’. Here, we interpret subdaily ‘lags’(hours) between FA and SR, reported by either isotopeapproaches or flux-based measurements, by exploring thephase difference (‘time lag’) within the 1 d time period. Allanalyses were performed using MATLAB R2007a (TheMathWorks, Inc., Natick, MA, USA) and wavelet analysissoftware (Torrence & Compo, 1998; Grinsted et al., 2004).

Data analysis

We explored the influence of FA or Ts on SR using waveletcoherence analysis. The assumption from a time series anal-ysis approach is that, if SR responds strongly and rapidly toa change in FA (in comparison with Ts), it might beexpected that Ts may have less of a role in controlling SR.

We tested the main hypothesis that FA influences SRindependent of changes in Ts and soil CO2 diffusivity. It isimportant to recognize that the diurnal cycle of solar radia-tion governs the daily course of air temperature,Ts and FA,which are drivers of SR. In addition, variations in soil watercontent (SWC) change the diffusivity of CO2 and thus SRrates (Simunek & Suarez, 1993), contributing to confound-ing effects. Therefore, changes in Ts and CO2 diffusivitycould mask or overestimate the relationship between FA andSR because there could be spurious correlations. Thus, weanalyzed the temporal correlation between SRr (represent-ing Ts and CO2 diffusion time series independent of SR)and FAr (Ts time series independent of FA).

First, we removed the effect of changes in Ts on FA by fit-ting independent simple linear regressions for each daycalculated from hourly measurements with the form:

FAr ¼ FA � ðB1 þ B2TS Þ Eqn 1

where B1 and B2 are parameters evaluated for each singleday during the growing season based on hourly measure-ments of Ts (at the depth of maximum correlation withSR). The depth of maximum correlation of Ts with SR wascalculated throughout the growing season, rather than foreach single day, to avoid the inclusion of periodicities as aresult of changes in heat transfer in the soil at each site. Thegoal of this first equation was to remove the periodicitiesin FA associated with changes in Ts that also influenceSR and could be a source of spurious temporal correlations.In other words, the FA signal was detrended for changesin Ts.

Second, we removed the effect of changes in Ts and CO2

diffusion on SR using:

SRr ¼ SR � ½ðB3expðB4�Ts ÞÞf Ds � Eqn 2

where B3 and B4 are parameters evaluated for each singleday during the growing season based on hourly measure-ments of Ts (at the depth of maximum correlation withSR), and fDs represents a function of diffusivity of soil CO2

in the soil profile calculated using the Moldrup model(Moldrup et al., 1999):

Ds

Da¼ /2 e

/

� �bS

Eqn 3

where Da is the molecular diffusivity of CO2 in the air, e isthe air-filled porosity, b is a constant (b = 2.9), S is the per-centage of silt plus sand content and U is the soil porosity.Thus, independent regressions with the form of Eqn 2 werefitted for each day during the growing season, calculatedfrom hourly measurements, as performed for FAr. In otherwords, the SR signal was detrended for changes in Ts andthe diffusivity of soil CO2.

Using this conservative approach, we propose that anytemporal correlation between FAr and SRr (residuals of FA

and SR) is likely to represent a link between FA and SR byremoving the effects of changes in temperature and CO2

diffusion in the soil. Importantly, we used the same depthof Ts for SRr and FAr to avoid the inclusion of artificial peri-odicities and lags as a result of differences in the time seriesof Ts as a response to heat transfer in the soil at each site.Absolute values of FA and SR are not the goal and are notrelevant in this study because the interpretations are per-formed in the frequency domain.

Results

Temporal relationships between SR and FA

Measurements of FA, Ts, SWC and SR showed large varia-tion in temporal patterns during the growing seasons at allstudy sites in the time domain (Fig. 1). Importantly, thesites showed a wide range of patterns for these variables as aresult of differences in climate and plant phenology. Thewavelet coherence analysis showed that the strongest syn-chrony between FA and SR was at the 1 d time periodacross study sites (Fig. 2a–d; Table 3). This was inferred byextracting the percentage of days with significant temporalcorrelations (see the Materials and Methods section andMethods S1) between FA and SR within the growing sea-son. The dark gray areas in Fig. 2 represent the regions withsignificant temporal correlations. Within forest sites, theMediterranean site showed the least synchrony at the 1 dtime period (24% significant days during the growing sea-son), followed by the temperate site with 52% significantdays, and the boreal site with nearly 83% significant days

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during the growing season (Table 3). The grassland siteshowed significant synchrony at the 1 d time period fornearly 56% of the days during the growing season(Table 3). Time periods longer than 1 d (i.e. 4, 8 and 12 d)also showed significant temporal correlations, but most ofthe synchrony was localized at time periods of less than12 d (Fig. 2a–d; Table 3). At any time period, the darkgray areas (showing significant correlations in Fig. 2) werenot continuous throughout the analyzed period, as gapswere found between them. In other words, at any site andtime period, the temporal correlation between SR and FA

was not constant throughout the growing season.An advantage of wavelet coherence analysis is the calcula-

tion of the phase difference (time lags) between two timeseries. As explained earlier, the phase difference representswhether or not two time series tend to oscillate simulta-neously at a given time period (in phase, showing no timelags) or rise and fall out of phase within a given time period(out of phase, showing a time lag between them). Thearrows in Figs 3 and 4 represent the phase difference.Overall, SR and FA were in phase (no time lags) at timeperiods greater than 1 d at all sites (Table 3). By contrast,FA preceded SR by between 3 and 7 h (out of phase) withinthe 1 d time period in the forest sites, but was mostly inphase (0.9 ± 3.9 h) at the grassland site (Table 3). At the1 d time period, the phase difference (time lag) was notconsistent throughout the growing season, as represented by

the standard deviation of the phase difference (time lags) inTable 3. In other words, the oscillation between the twotime series at the 1 d time period was not constant through-out the growing season as the phase difference variedamong days.

Temporal relationships between SR and Ts

We found a strong synchrony at the 1 d time periodbetween SR and Ts at all sites, but significant temporal cor-relations were also found at larger time periods (Fig. 2e–h).The least synchrony at the 1 d time period was found at theMediterranean site, followed by the temperate and borealforests, with nearly 26%, 58% and 76% significant days,respectively, during the growing season (Table 3). Thegrassland site showed synchrony at the 1 d time period fornearly 50% of the days during the growing season(Table 3). Other time periods larger than 1 d (i.e. 4, 8, 12and 16 d) also showed significant temporal correlation, butmost of the synchrony was localized at time periods of lessthan 12 d (Fig. 2e–h). At any site and time period, the tem-poral correlation between SR and Ts was not constantthroughout the growing season.

Overall, SR and Ts were in phase (no time lags) at timeperiods larger than 1 d. By contrast, SR preceded Ts bybetween 5 and 7 h in the forest sites, and was mostly inphase (1 ± 3.9 h) at the grassland site, within the 1 d time

(a) (e)

(f)

(g)

(h)

(b)

(c)

(d)

Fig. 2 Wavelet coherence analysis and phasedifference between canopy photosynthesis(FA) and soil CO2 efflux (SR), or SR and soiltemperature at the depth of maximumcorrelation with SR (Ts). The approximatephase difference is shown by arrows, inphase pointing right and out of phasepointing left. The shades for power valuesare from white (low values) to dark gray(high values). Black contour lines representthe 5% significance level, and the thick blackline indicates the cone of influence thatdelimits the region not influenced by edgeeffects. Days of the year (DOY), days afterJanuary 1st of the year in which data werecollected.

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period (Table 3). At the 1 d time period, the phase differ-ence (time lag) was not constant throughout the growingseason, and is represented by the standard deviation of thephase difference (time lags) in Table 3.

Temporal relationships between SR and FA accountingfor confounding effects

To test the hypothesis that FA influences SR independent ofvariation in Ts and soil CO2 diffusivity (i.e. confoundingeffects), we tested the temporal correlation between SRr andFAr. In general, we found a decrease in the temporalsynchrony between SRr and FAr at the 1 d time period(Fig. 3), in comparison with the temporal correlation atthat time period between SR and FA (Fig. 2a–d). The leastsynchrony at the 1 d time period was found at theMediterranean and temperate sites, followed by the borealforest, with nearly 30%, 30% and 60% significant days,respectively, during the growing season (Table 3). Thegrassland site showed synchrony at the 1 d time period fornearly 39% of the days during the growing season

(Table 3). Importantly, at any site and time period, thetemporal correlation between SRr and FAr was not constantthroughout the growing season.

The influence of FAr on SRr at the 1 d time period wasindependent of changes in Ts or soil moisture across studysites (Fig. 4). Furthermore, it was independent of the mag-nitude of FAr at the forest sites, but was dependent on themagnitude of FAr at the grassland site. For the grassland site,days with significant temporal correlation between SRr andFAr showed significantly higher FAr than days withoutsignificant temporal correlation (t-test, P = 0.0039).

When calculating the phase difference (time lags)between SRr and FAr, our results were consistent with previ-ous observations for SR and FA. Overall, SRr and FAr werein phase (no time lags) at time periods of more than 1 d atall sites (Table 3). We found that FAr was out of phase atthe forest sites as it preceded SR by between 5 and 11 hwithin the 1 d time period. By contrast, this relationshipwas mostly in phase (no time lags) at the grassland sitewithin the 1 d time period (Table 3). Similarly, within the1 d time period, the phase difference (time lag) was not

Table 3 Percentage and mean phase differences or time lags (± 1 SD) within days with significant correlation between soil CO2 efflux andcanopy photosynthesis (SR–FA), soil CO2 efflux and soil temperature (SR–Ts) or residuals of soil CO2 efflux and canopy photosynthesis(SRr–FAr) during the growing season

Time-period Site ID

SR–FA SR–Ts SRr–FAr

% of days Time lag (h) % of days Time lag (h) % of days Time lag (h)

1 d US-Ton 23.8 )3.0 ± 1.1 26.6 6.9 ± 1.2 29.9 )5.7 ± 1.5US-Moz 51.6 )7.6 ± 2.4 58.2 6.9 ± 2.2 30.8 )11.8 ± 3.0FI-Hyy 82.9 )4.0 ± 0.8 75.7 5.1 ± 1.2 60.4 )5.1 ± 1.2AT-Neu 55.7 )0.9 ± 3.9 49.5 1.0 ± 3.9 38.8 )0.8 ± 5.3

2 d US-Ton 0.5 0 2.4 0 16.4 0US-Moz 2.7 0 9.3 0 10.7 0FI-Hyy 0 0 1.4 0 0 0AT-Neu 9.9 0 21.2 0 13.0 0

4 d US-Ton 4.9 0 0 0 7.2 0US-Moz 0 0 12.5 0 0 0FI-Hyy 0 0 5.8 0 16.8 0AT-Neu 18.2 0 9.0 0 4.7 0

8 d US-Ton 0 0 0 0 0 0US-Moz 7.6 0 23.25 0 0 0FI-Hyy 0 0 0 0 0 0AT-Neu 6.3 0 13.7 0 0 0

12 d US-Ton 0 0 0 0 0 0US-Moz 31.5 0 37.6 0 32.8 0FI-Hyy 0 0 0 0 0 0AT-Neu 0 0 0 0 0 0

16 d US-Ton 0 0 0 0 0 0US-Moz 0 0 0 0 15.6 0FI-Hyy 0 0 0 0 0 0AT-Neu 0 0 5.6 0 0 0

Results are extracted from the dark gray areas in the wavelet coherence analysis of Figs 3 and 4. Ts, soil temperature at the depth of maximumcorrelation with SR at each site (US-Ton, 16 cm depth; US-Moz, 10 cm depth; FI-Hyy, 2 cm depth; AT-Neu, 5 cm depth). For details on thecalculation of SRr–FAr, see the Materials and Methods section. US-Ton, Mediterranean deciduous forest; US-Moz, temperate broadleaf forest;FI-Hyy, boreal evergreen forest; AT-Neu, temperate grassland.A negative time lag means that the response of the first variable is behind, by x number of hours, the response of the second variable.

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constant throughout the growing season, and is representedby the standard deviation of the phase difference (time lags)in Table 3.

Discussion

Our findings based on time series analysis show that FA

influences SR at multiple temporal scales during the grow-ing season at three forest sites with different climates and ata temperate grassland. Importantly, the temporal correla-tions between FA and SR (at any time period), and thephase difference (time lags) with the 1 d time period, wereneither uniform nor constant throughout the growing sea-son at any study site.

These results suggest that: (1) the link between FA andSR may not be constant throughout the growing season;and (2) different drivers (e.g. photosynthesis, soil CO2 dif-fusion, Ts, phloem transport) that influence the allocationand transport speed of carbon through the soil–plant–atmosphere continuum are likely to coexist within a

growing season, explaining the multiple time periods andtime lags observed at the study sites.

The temporal correlation between FA and SR was mostconsistent at the 1 d time period for all vegetation types.This suggests an influence of daily photosynthesis on SRand supports the observations from different methods inforests (Baldocchi et al., 2006; Hogberg et al., 2008; Subkeet al., 2009) and grasslands (Staddon et al., 2003; Carbone& Trumbore, 2007; Bahn et al., 2009). Furthermore, thephase difference (time lag) at the 1 d time period providesinsights into the nature and origin of coupling betweenthese processes. This is supported because the delay betweentwo time series could provide information on the couplingbetween the processes, and causality is inferred under theassumption that the effect must follow the cause. For exam-ple, in forests, FA increases before SR, suggesting twopotential mechanisms: (1) a fast transport of recent photo-synthate carbon molecules from the canopy to the forestsoil (Hogberg et al., 2008; Dannoura et al., 2011); or (2)the propagation of pressure concentration waves in thephloem of these tall trees (Mencuccini & Holtta, 2010).Importantly, pressure concentration waves may be presentonly when the osmotic pressure is high relative to turgordifferences, and is highly variable among species(Thompson & Holbrook, 2003). In grasslands, the phasedifference (near zero lags) supports the observation of astrong link between recent photosynthetic products and SRat the 1 d time period (Bahn et al., 2009).

The fact that SR responds ahead of Ts at the 1 d timeperiod in forests could be interpreted as the combination ofthe following: (1) temperature may have less of a role incontrolling SR at this time period during the growing sea-son in forests; and (2) autotrophic respiration maydominate the SR signal during the growing season inforests. By contrast, SR is nearly in phase with Ts in thegrassland at the 1 d time period. These results indicate thatautotrophic respiration dominates during the growingseason, but this contribution is highly variable (Epron et al.,2001; Irvine et al., 2008; Ruehr & Buchmann, 2010).Furthermore, this variability indicates that the synchronybetween FA and SR is not constant within the growingseason (Fig. 3).

It is important to consider the potential confoundingeffects of soil CO2 diffusivity and Ts on SR. Without con-sidering changes in these variables, the influence of FA onSR can be over-represented at most sites. This can beobserved by comparing the significant temporal correlation(dark gray areas) between Fig. 2(a–d) and Fig. 3. Thus, thisstudy emphasizes the importance of incorporating the effectof Ts and soil CO2 diffusivity to avoid misinterpretation ofthe temporal correlation and potential confounding effects(Davidson et al., 1998; Stoy et al., 2007). By incorporatingthe effects of changes in Ts and soil CO2 diffusivity, weobserved a reduced but still important correlation between

(a)

(b)

(c)

(d)

Fig. 3 Wavelet coherence analysis and phase difference betweensoil CO2 efflux (SRr) and canopy photosynthesis (FAr) after removingthe effect of soil temperature and soil CO2 diffusivity for soil CO2

efflux, and soil temperature for canopy photosynthesis. For detailson the calculation of SRr and FAr, see the Materials and Methodssection. The approximate phase difference is shown by arrows, inphase pointing right and out of phase pointing left. The shades forpower values are from white (low values) to dark gray (high values).Black contour lines represent the 5% significance level, and the thickblack line indicates the cone of influence that delimits the region notinfluenced by edge effects. Days of the year (DOY), days afterJanuary 1st of the year in which data were collected.

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FAr and SRr (Fig. 3). Although the temporal correlationwas reduced, our results show that the generality of the con-clusions is consistent with the initial approach (relationshipbetween FA and SR; Fig. 2a–d; Table 3).

It is critical to recognize that the time lags at the 1 d timeperiod are not constant over the growing season (expressedas standard deviations in Table 3 and by the arrows inFigs 2 and 3). Recent reviews have compiled informationabout forests and grasslands, reporting mean time lagswithin the 1 d time period (Kuzyakov & Gavrichkova,2010; Mencuccini & Holtta, 2010) that are consistent withthose given in Table 3. However, most of the studies (iso-tope- or flux-based) compiled by these reviews have focusedtheir attention at only one particular time (i.e. isotope-based studies), or are limited by the time series analysisemployed (i.e. flux-based studies using cross-correlation orFourier analysis), limiting the capacity to explore the varia-tion across the growing season. A possible explanation forthe variation in time lags within the 1 d time period is theresponse to the daily variation in stomatal conductance, car-bon storage effects in plants and changes in photosynthesisduring the course of the growing season (Hartley et al.,

2006) as a result of drought stress (Ruehr et al., 2009). Ourresults show that the influence of FA on SR at the 1 d timeperiod occurs under multiple environmental conditions.Only at the grassland site were higher photosynthesis ratesassociated with significant temporal correlation with SR(Fig. 4). This could be explained by the fast transport ofcarbon in grasslands controlled by photosynthesis, andtherefore the sensitivity to changes in environmental condi-tions, such as shading (Bahn et al., 2009). We believe thatthese results raise research questions on why, when and howthese relationships occur across different ecosystems andtime scales under nonstationary weather conditions andwith future climate variability.

Our results show that, by using time series analysis inconjunction with continuous efflux measurements, fromeither automated chambers or networks of soil CO2 gradi-ents, it is possible to explore the temporal correlationbetween FA and SR. Our results are novel because they rec-oncile apparent discrepancies from isotope-based and flux-based observations. As discussed earlier and in recentreviews (Kuzyakov & Gavrichkova, 2010; Mencuccini &Holtta, 2010), different methods may identify different

(a)

(b)

(c)

(d)

Fig. 4 Normalized time series of canopy photosynthesis (FA), soil temperature, soil water content and soil CO2 efflux (SR) across the growingseason at the study sites. The gray areas show days with significant temporal correlation between CO2 efflux (SRr) and canopy photosynthesis(FAr) at the 1 d time period extracted from Fig. 3. Normalization was based on Eqn 5 in Supporting Information Methods S1 with the form:X = [X)(mean(X))] ⁄ std(X), where X represents the values of the time series analyzed (e.g. soil CO2 efflux or FA). Days of the year (DOY), daysafter January 1st of the year in which data were collected.

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mechanisms on how FA influences SR. In this study, weshowed that, from a time series approach, it is possible toidentify all the time periods and time lags associated withthese fluxes, as reported by previous studies (seeIntroduction). However, the multi-temporal correlations intime periods and time lags are not uniform throughout thegrowing season, showing that the strong link between FA

and SR is not constant in time. Further research is neededto obtain a comprehensive SR theory that considers themulti-temporal influence of biological (i.e. photosynthesis)and physical (i.e. soil CO2 diffusion, Ts) drivers on SR.

Potential limitations and future considerations

Our study presents an advance over previous analyses usingFourier transform and cross-correlation techniques to studythe influence of FA on SR, because they fail in the presenceof nonstationary phenomena, such as rain pulses and heatwaves, that are present during a growing season (Katulet al., 2001). Wavelet analysis overcomes this issue by usinga window size that is not fixed, and varies as a function offrequency, with an optimal trade-off between time and freq-uency resolution. An advantage of wavelet coherenceanalysis is that it finds regions in time and frequencydomains in which two time series co-vary, but do not neces-sarily have high common power (Grinsted et al., 2004). Asa disadvantage, the fact that these two time series may notnecessarily have high common power could lead to an over-interpretation of the magnitude of the temporal influenceof FA on SR. Furthermore, our analysis may not have beenable to remove all the influence of physical factors (i.e. Ts,soil CO2 diffusivity) on the periodicity of the signals, andmay show temporal correlations where there are none (Stoyet al., 2007). We tried to overcome this limitation byremoving the effects of Ts and soil CO2 diffusivity by fittingindependent equations for each day and by limiting ourstudy to the growing season. Using a different depth of Ts

(other than that with the highest correlation) in these fittingequations changes the temporal relationships as a result ofthe introduction of a heat transfer component into thesignal processing (Vargas et al., 2010c), but does not changethe overall conclusion of the multi-temporal relationshippresented in this study.

Because biophysical factors influence FA and SR at multi-ple temporal scales, multiple approaches are needed tobetter understand the temporal correlation between thesefluxes (Bahn et al., 2010). Most isotope labeling studieshave been performed on short-term campaigns and theirresults have focused on the identification of the correlationbetween FA and the recovery of the isotope signal via SR.These studies are expensive and difficult to perform; how-ever, future campaigns could be longer or repetitive acrossseasons to track carbon molecules and identify fast and slowtransport rates under different weather conditions (i.e. non-

stationary) and FA rates. Repeated labeling, coupled withflux-based measurements (e.g. eddy covariance, soil CO2

flux gradients and automated SR chambers) and the use oftime series analysis, could help in our understanding of thefate of recently assimilated carbon and its role on SR.Finally, long-term deployment of isotope and CO2 flux(plant and soil) measurements (Wingate et al., 2010), withmanipulations of photosynthesis (Bahn et al., 2009) orphysical properties of the soil (e.g. changes in SWC)(Thomey et al., 2011), may enable a better understandingof the above-ground links with SR at multiple temporalscales.

Acknowledgements

D.D.B. and R.V. acknowledge the help and support ofSiyan Ma, and P.J.H., K.P.H. and B.Y. acknowledge thehelp and support of Steven Pallardy with field measure-ments. R.V. and D.D.B. were supported by the NationalScience Foundation grant DEB-0639235. P.J.H. and B.Y.’sresearch was supported by US Department of Energy,Office of Science, Biological and Environmental Research(BER), as a part of the Terrestrial Carbon Processes (TCP)Program and conducted at Oak Ridge National Laboratory(ORNL), managed by UT-Battelle, LLC, for the USDepartment of Energy under contract DE-AC05-00OR22725. J.P. and L.K. acknowledge support from theAcademy of Finland Centre of Excellence program and pro-ject numbers 130984, 218094, 213093 of the Academy ofFinland. M.B. acknowledges help by Michael Schmitt andKarin Bianchi and support from the Austrian Science Fundgrant FWF P18756-B16.

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Supporting Information

Additional supporting information may be found in theonline version of this article.

Methods S1 Soil CO2 efflux measurements and waveletanalysis.

Please note: Wiley-Blackwell are not responsible for thecontent or functionality of any supporting informationsupplied by the authors. Any queries (other than missingmaterial) should be directed to the New Phytologist CentralOffice.

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